Grade 6 Summer Math Packet
I.
Place Value
Ten
One
Hundred
Ten
One
Hundred
Ten
One
Hundred
Ten
One
ONES
Hundred
THOUSANDS
One
MILLIONS
Ten
BILLIONS
Hundred
TRILLIONS
1
2
3,
4
5
6,
7
8
9,
0
1
2,
3
4
5
The number displayed is pronounced, “One hundred twenty-three trillion, four hundred fifty-six billion, seven
hundred eighty-nine million, twelve thousand, three hundred forty-five.”
Write the place value of the underlined digit.
1). 1,845,745,321 ________________________
2). 438,382
______________________
Write the number in standard form (as a number!).
3). Nine hundred two thousand, five hundred thirteen
__________________________
4). Twenty million, forty-six thousand, seven
__________________________
Round each number to the indicated place value.
5). 750,936,593; hundred million
___________________________
6). 39,404,783,549; billion
___________________________
Compare the following numbers using < , > , or = .
7). 50,385,767 _______
50,358,776
Order the following number s from least to greatest.
9).
825,403; 825,340; 825,430; 825,304; 582,430
10). 1746; 6471; 4716; 7164; 4167
8).
83,762,628,302 _______ 83,672,320
II.
Decimal Place Value
Thousandths
Hundredths
Tenths
Ones
3
4
5
Hundred
Thousands
2
Ten
Thousandths
1
Tens
Hundreds
ONES
7
8
6
The number displayed is pronounced, “One hundred twenty-three AND forty-five thousand, six hundred
seventy-eight hundred thousandths.”
Write the place value of the underlined digit.
11).
184.5321 ________________________
12). 2.85067
_______________________
Write the decimal number in standard form (as a number!).
13).
Four and seventy-six thousandths
__________________________
14).
Three thousand, eight hundred fifty-five ten thousandths
__________________________
Round each decimal number to the indicated place value.
15).
12.3456; thousandth
___________________________
16).
347.9148; hundredth
___________________________
17).
5.9731; tenth
___________________________
Compare the following numbers using < , > , or = .
18). 12.345 _______
123.45
19).
5.074 _______ 5.08
Order the following number s from least to greatest.
20).
6.7821; 67.821; 6.2871; 6.2187; 67.281
21).
0.9; 0.062; 0.43; 0.407; 0.08
III. Mental Math Strategies
Compatible Numbers: pairs of numbers that can be computed easily together.
*Combine compatible numbers, and then combine what remains.
22).
25 + 18 + 75 =
23).
30 + 58 + 160 + 10 =
Patterns:


When multiplying numbers that end in zeros, multiply the non-zero parts and add one zero to
your answer for each zero in the problem.
When dividing numbers that end in zeros, divide the non-zero numbers and add zeros for the
difference of the zeros in the dividend and the divisor.
24).
20 × 700 =
25).
12,000 × 60 =
26).
5,400,000 ÷ 900 =
27).
5600 ÷ 80 =
IV. Whole Number Estimation
Estimating Sums and Differences
When estimating sums, it’s typically easiest to round both numbers to the nearest ten or hundred before adding.
28).
Estimate the sum of 28 and 114.
29).
Estimate 1567 + 789.
When estimating differences of large numbers, it’s typically easiest to round both numbers to the nearest hundred
before subtracting.
30).
Estimate the difference of 208 and 114.
31).
Estimate 4132 – 2497.
Estimating Products and Quotients
When estimating products, you should round the numbers to the place value of their leading digits. The leading digit
of a whole number is the first digit at the left.
32).
Estimate the product of 123 × 41.
33).
Estimate 62 × 819.
When estimating quotients, look for compatible numbers, which are numbers that will make the calculation easier.
Knowing your multiplication and division facts will help make this estimation easy!
34).
Estimate the quotient of 552 ÷ 67.
V.
Decimal Estimation
35).
Estimate 2743 ÷ 36.
When estimating with decimals, first round them to the nearest whole number, then follow the same
techniques used for whole number estimation!
36).
865.32 + 71.98
37).
421.09 – 315.78
38).
34.5 × 76.2
39).
247.6 ÷ 48.75
VI. Whole Number Operations
Simplify the expression. Line up your problems vertically (up and down) to complete the problems more easily!
40). 827 + 2098
41).
3,598 – 276
42).
4,488 + 29 + 673
43). 6,003 – 855
44).
7,300 – 1,339
45).
3482 + 639 + 483
46).
47).
821 × 5
48).
409 × 32
76 × 14
49).
87 ÷ 4
50).
645 ÷ 15
51).
1050 ÷ 25
VII. Adding and Subtracting Decimal Numbers
Simplify the expression. Rewrite the problems vertically, and make sure you line up your decimal points!
52). 57.3 + 21.4
53).
55). 0.64 + 9.213
56).
58). 52.68 – 7.351
59).
3.127 + 416.89
84.615 – 62.13
123 – 4.76
54).
34 + 72.15
57).
459.16 – 72
60).
53 + 12.34 – 11.8
VIII. Fractions
Equivalent Fractions
61). Write two equivalent fractions for
6
7
.
_________
_________
62). Write two equivalent fractions for
2
5
.
_________
_________
Fractions in Simplest Form
Write each fraction in simplest form.
63).
18
54
64).
20
64
65).
12
35
66).
Improper Fractions and Mixed Numbers
Write the mixed number as an improper fraction.
67).
𝟒
7𝟗
68).
𝟖
𝟑
3 𝟏𝟓
69).
6𝟒
𝟗𝟒
𝟏𝟏
72).
𝟓𝟏
𝟖
Write the improper fraction as a mixed number.
70).
𝟓𝟏
𝟕
71).
Adding and Subtracting Fractions with Common Denominators
Add or subtract. Write your answers in simplest form.
73).
1
9
75).
7
12
5
+9
3
− 12
74).
76).
9
4
− 10
10
6
7
5
+7
14
70